Author(s): Y. Xu; Y. Song; X. Liu
Linked Author(s): Yuntian Song, Yi Jun Xu, Xuan Liu
Keywords: Local scour; Immersed boundary method; OpenFOAM; ibScourFoam; Bridge pier; Morphodynamics
Abstract: Scour around a simple vertical cylinder has been numerically investigated by many researchers, most of which used the moving mesh technique to track the bed morphological changes. However, this method is limited by the in-stream structure complexity. Even for the simple cases of bridge piers, they may have multiple columns, footings, and piles. For example, as the scour hole around the pier develops, the pier foundation may experience burial or exposure, which is very difficult to be tracked by the grid point movement. In the literature, Flow-3D was reported to simulate the local scouring process around a bridge pier with multiple columns. However, this study only considered the interaction of the bed with vertical piles, which simplified the case. To advance our understanding of sediment transport and to help engineering design, a more sophisticated, robust, and yet computationally affordable model is needed. An alternative for tracking the bed evolution is the immersed boundary (IB) method, where the computational mesh is fixed, and the wall boundary is represented by a 2D surface. Special treatment is performed to reflect the flow behavior near the immersed boundaries. In this work, a novel 3D local scour model, named as ibScourFoam, is proposed based on immersed boundary (IB) method. The scour model was developed in OpenFOAM. The in-stream structure is captured with body-fitted mesh, and the bed is treated as immersed boundary (IB). The scour model contains three parts: the pre-processing of IB information required by the IB method, the flow solver (modified from pisoFoam) with a special IB wall treatment, and the bed morphodynamic solver based on an unstructured triangulated mesh, which is used as IB for the flow solver. A simple sand-slide algorithm is also applied in the present scour model, which uses a modified diffusion equation for bed elevation to smooth out the excessive bed angles if they are larger than the repose angle. The bed-load transport is related to the gradient of bed shear or shear velocity. In order to obtain accurate distribution of wall shear stress on IB surface, a special wall model is utilized, where shear velocity is calculated through iterative solution of velocity profiles. The key of the coupling process is to map the bed shear stress from 3D hydrodynamics computational domain (3D hydro mesh) to 2D morphodynamics computational space (2D morpho mesh). A generic searching algorithm is used to determine the interpolation stencil for the mapping process. A straightforward treatment in finite volume method is to store τb and to calculate qb on cell centroids in a 2D morpho mesh. However, based on the Gauss’s theorem, the edge value of qb is actually used in the divergence calculation. Therefore, it is suggested that edge center storage is used for the variable of τb on the 2D morpho mesh. Besides, a robust geometric intersection algorithm was developed to handle complex in-stream structures, as well as optimized parallelization. This scour model was firstly validated by a classic pier scour case. Then, it was used to simulate the flow and scour around a horizontal cylinder with a complex foundation, which turned out to match well with the experimental results.
Year: 2024